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Canadian Raising with Language-Specific Weighted Constraints Joe Pater, University of Massachusetts Amherst Canadian raising with language-specific weighted constraints Joe Pater, University of Massachusetts Amherst The distribution of the raised variants of the Canadian English diphthongs is standardly analyzed as opaque allophony, with derivationally ordered processes of diphthong raising and of /t/ flapping. This paper provides an alternative positional contrast analysis in which the pre-flap raised diphthongs are licensed by a language-specific constraint. The basic distributional facts are captured with a weighted constraint grammar that lacks the intermediate level of representation of the standard analysis. The paper also provides a proposal for how the constraints are learned, and shows how correct weights can be found with a simple, widely used learning algorithm.* 1. Introduction In Canadian English, the diphthongs [ai] and [au] are famously in near-complementary distribution with raised variants [ʌi] and [ʌu]. For the most part, the raised diphthongs occur only before tautosyllabic voiceless consonants (1a.), with their lower counterparts occurring elsewhere (1b.). The distribution overlaps only before the flap [ɾ] (1c.). (1) a. [sʌik] psych [rʌit] write [lʌif] life [hʌus] house b. [ai] I [raid] ride [laivz] lives (pl.) [hauz] house (v.) c. [mʌiɾɚ] mitre [saiɾɚ] cider [tʌiɾl] title [braiɾl] bridle [rʌiɾɚ] writer [raiɾɚ] rider As Idsardi (2006) points out, analyses of CANADIAN RAISING (Chambers 1973) are generally of two types: those that treat the low/raised diphthong distinction as phonemic (Joos 1942), and those that treat it as opaquely allophonic, with the surface vowel contrast derived from the underlying contrast between /t/ and /d/ that is itself neutralized to the flap (Harris 1951/1960). The standard analysis is that of Chomsky 1964, in which the rule that raises underlying /ai/ and /au/ to [ʌi] and [ʌu] before voiceless consonants applies before the rule changing underlying /t/ to [ɾ], producing derivations like /taitl/ → tʌitl → [tʌiɾl]. In this paper, I pursue a third type of analysis, intermediate between the phonemic and allophonic approaches, in which the distribution of these diphthongs is an instance of positionally restricted contrast (see Mielke et al. 2003 for an earlier positional contrast analysis).1 * Thanks especially to Paul Boersma for his collaboration on an earlier presentation of this research (Boersma and Pater 2007), and to Michael Becker, Elliott Moreton, Jason Narad, Presley Pizzo and David Smith for their collaboration on versions of the constraint induction procedure described in section 3. Thanks also to Adam Albright, Eric Baković, Ricardo Bermúdez-Otero, Jack Chambers, Heather Goad, Bruce Hayes, Bill Idsardi, Karen Jesney, John McCarthy, Robert Staubs and Matt Wolf for useful discussion, as well as participants in Linguistics 751, UMass Amherst in 2008 and 2011, and at NELS 38, University of Ottawa, and MOT 2011, McGill University. This research was supported by grant BCS- 0813829 from the National Science Foundation to the University of Massachusetts Amherst. 1 Mielke et al. (2003) restrict the distribution of by disallowing voiced consonants after [ʌi] and [ʌu], and voiceless consonants after [ai] and [au]. This analysis fails to capture the ill-formedness of [ʌi] and [ʌu] The first apparent challenge for this approach is that the environment for the contrast is phonetically unnatural: the flap has no known phonetic property that makes raised diphthongs easier to produce or perceive before it. This is a problem, of course, only if phonological rules or constraints are limited to those that are phonetically grounded. Such a limit has long been known to be untenable (Bach and Harms 1972, Anderson 1981). In particular, there are well- documented instances of productive phonological patterns that do not have a synchronic phonetic basis (see e.g. Icelandic velar fronting in Anderson 1981, NW Karaim consonant harmony in Hannson 2007, and Sardinian [l] ~ [ʁ] alternations in Scheer 2014; see also Hayes et al. 2009 for discussion and experimental work). Furthermore, experimental studies have found little, if any, evidence that phonetically grounded patterns enjoy a special status in learning, although other factors, such as structural simplicity, have a consistent effect (see Moreton and Pater 2012 for an overview). In the analysis to follow, pre-flap raised diphthongs are licensed by a language- specific phonetically arbitrary constraint. A second potential challenge for an analysis of Canadian raising with positional contrast is to rule out raised diphthongs in environments other than those of a following voiceless obstruent or flap. I show that it is possible to properly restrict the distribution of raised diphthongs with a small set of constraints, if those constraints are weighted, as in HARMONIC GRAMMAR (HG; Smolensky and Legendre 2006; see Pater 2009, 2014, for an introduction and overview of other research in this framework). This paper also includes a proposal for how the constraints in HG are learned. I adopt a broadly used on-line learning algorithm that Boersma and Pater (2014) refer to as the HG-GLA. In the proposed extension to constraint induction, constraints are constructed from differences between the structure of the observed forms and the learner’s “mistakes”. I illustrate this approach using a simplified version of the distribution of Canadian English diphthongs. The analysis makes use of only a single mapping from underlying representation (UR) to surface representation (SR), with no intermediate derivational levels, as in standard optimality theory (OT: Prince and Smolensky 1993/2004). Some other basic assumptions differ from those of standard OT: the constraints are weighted, rather than ranked, and the constraints are language-specific and sometimes phonetically arbitrary, rather than universal and substantively grounded. This diverges from approaches to the distribution of the raised diphthongs and to other instances of ‘counterbleeding opacity’ that maintain OT's ranking and universality but enrich its derivational component (see Bermúdez-Otero 2003 on Canadian English, and McCarthy 2007 and Baković 2011 on opacity, derivations and OT). In the conclusion, I discuss some directions for further research that may help to tease apart future theories of the representation and learning of patterns like Canadian raising. 2. Analysis The basic distribution of the diphthongs can be analyzed by adapting to HG the standard OT approach to allophony (see McCarthy 2008 for a tutorial introduction). The first ingredient in the analysis is a constraint that prefers the phones with the broader distribution, here [ai] and [au], by penalizing the contextually restricted variants, here [ʌi] and [ʌu]. This constraint, *RAISED, conflicts with a context-specific constraint against the sequence of a low diphthong and tautosyllabic voiceless consonant, *(LOW, VOICELESS). The tableau in (2) shows the situation in when no consonant follows, and generates voicing alternations, rather than raising (see Idsardi 2006 on the productivity of raising). 2 which *(LOW, VOICELESS) has its effect, in choosing a raised diphthong before a voiceless consonant. (2) *(LOW, VOICELESS) > *RAISED + IDHEIGHT *(LOW, VOICELESS) *RAISED IDHEIGHT H /saik/ 4 2 1 ☞ [sʌik] –1 –1 –3 [saik] –1 –4 The input UR for psych [sʌik] is assumed to have low diphthong, from psychology with [ai] (this could equally be a richness of the base tableau – see (3) below). Violation counts are shown in the tableaux as negative integers. The correct SR violates the faithfulness constraint penalizing a change in diphthong height, IDHEIGHT, as well as *RAISED. Its competitor [saik] violates only *(LOW, VOICELESS). In HG, the well-formedness, or HARMONY of a representation is the weighted sum of its violation scores, shown in the column labeled H in the tableau. In an OT-like categorical version of HG, the optimum is the candidate with the highest Harmony. For [sʌik] to beat [saik], the weight of *(LOW, VOICELESS) must be greater than the summed weights of *RAISED and IDHEIGHT – this WEIGHTING CONDITION is shown as the caption of the tableau in (2). Weights meeting this condition are shown beneath the constraint names; in section 3 I will discuss one way of finding correct weights using a learning algorithm. If *RAISED has a greater weight than IDHEIGHT, underlying /ʌi/ and /aʌ/ will map to surface [ai] and [au]. This is illustrated in the tableau in (3) for underlying /ʌi/. (3) *RAISED > ID-HEIGHT *RAISED IDHEIGHT H /ʌi/ 2 1 [ʌi] –1 –2 ☞ [ai] –1 –1 This is a RICHNESS OF THE BASE tableau, showing that if the grammar is supplied with a raised diphthong that would surface in an inappropriate context, it will map it to the correct low diphthong. To license the contrast in pre-flap context, we need only add a constraint against low diphthongs in that environment, *(LOW, FLAP), which in HG can act in a gang effect with IDHEIGHT to counteract *RAISE. To show this, I use Prince’s (2000) comparative tableau format. The rows in (4) show the differences between the scores of the desired optima (or WINNERS) and their competitors (or LOSERS). The scores of the losers are subtracted from those of the winners, so that winner-preferring constraints display a positive number in the relevant row, while loser- preferring constraints display a negative value. For instance, the first row with Input /saik/ is based on the candidates in (2). The candidate with the raised diphthong, which is the winner here, has no violation of *(LOW, VOICELESS) while its competitor has one, so the comparative vector has +1. For *RAISED and IDHEIGHT the winner has a violation and the loser has none, and the vector shows –1. The second row corresponds to the tableau in (3), and the last two rows correspond to tidal and title, pronounced as [taiɾl] and [tʌiɾl] in Canadian English. 3 (4) Comparative HG tableaux Input W ~ L *(LOW, *RAISED *(LOW, IDHEIGHT ∑ VOICELESS) FLAP) 4 2 2 1 /saik/ [sʌik] ~ [saik] +1 –1 –1 +1 /ʌi/ [ai] ~ [ʌi] +1 –1 +1 /taiɾl/ [taiɾl] ~ [tʌitl] +1 –1 +1 +1 /tʌiɾl/ [tʌiɾl] ~ [taiɾl] –1 +1 +1 +1 As Prince (2000) explains, the comparative format is useful because the OT ranking conditions can be directly read from it.
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